In this paperwe construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counter examples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz c...

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators wh...

Given a close 3-form H ∈ Ω 0 (M), we define a twisted bracket on the space Γ(TM) ⊕ Ω 0 (M). We define the group of H-twisted Hamiltonian symmetries Ham(M, J;H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold, which leads to generalized complex reduction much the same way as symplectic reduction is constructed. The definitions a...

The Hamiltonian describing fermion pair production from an arbitrarily time-varying electric field in two dimensions is studied using a group-theoretic approach. We show that this Hamiltonian can be encompassed by two, commuting SU(2) algebras, and that the twodimensional problem can therefore be reduced to two one-dimensional problems. We compare the group structure for the two-dimensional pro...

LetF be a 2-factorization of the complete graphKv admitting an automorphism groupG acting primitively on the set of vertices. IfF consists of Hamiltonian cycles, thenF is the unique, up to isomorphisms, 2-factorization ofKpn admitting an automorphism group which acts 2-transitively on the vertex-set, see [A. Bonisoli, M. Buratti, G. Mazzuoccolo, Doubly transitive 2-factorizations, J. Combin.Des...

Let O be a quantizable coadjoint orbit of a semisimple Lie group G. Under certain hypotheses we prove that #(π1(Ham(O))) ≥ #(Z(G)), where Ham(O) is the group of Hamiltonian symplectomorphisms of O. MSC 2000: 53D05, 57S05, 57T20